76 citations · 123 across the 14 of their papers we have counts for
14 papers
A Numerical Investigation of the RayleighFaberKrahn Inequality for Polyhedral Domains
Josué D. Díaz-Avalos, Antoine Laurain
We present numerical results for the problem of minimizing the first Dirichlet eigenvalue of the Laplacian among three-dimensional convex polyhedra with a prescribed number of face…
FormOpt: A FEniCSx toolbox for level set-based shape optimization supporting parallel computing
Josué D. Díaz-Avalos, Antoine Laurain
This article presents the toolbox FormOpt for two- and three-dimensional shape optimization with parallel computing capabilities, built on the FEniCSx software framework. We introd…
Optimization of centroidal Voronoi tessellations
Ernesto G. Birgin, Juan S. C. Franco, Antoine Laurain
In this paper, we investigate the optimization of Centroidal Voronoi Tessellations (CVT) under geometric constraints. For this purpose, we minimize a linear combination of the stan…
Sensitivity analysis and tailored design of minimization diagrams
Ernesto G. Birgin, Antoine Laurain, Tiago C. Menezes
Minimization diagrams encompass a large class of diagrams of interest in the literature, such as generalized Voronoi diagrams. We develop an abstract perturbation theory and perfor…
Analysis and application of a lower envelope method for sharp-interface multiphase problems
Antoine Laurain
We introduce and analyze a lower envelope method (LEM) for the tracking of interfaces motion in multiphase problems. The main idea of the method is to define the phases as the regi…
A Shape-Newton approach to the problem of covering with identical balls
Ernesto G. Birgin, Antoine Laurain, Rafael Massambone +1
The problem of covering a region of the plane with a fixed number of minimum-radius identical balls is studied in the present work. An explicit construction of bi-Lipschitz mapping…
An abstract lagrangian framework for computing shape derivatives
Antoine Laurain, Pedro T. P. Lopes, Jean C. Nakasato
In this paper we study an abstract framework for computing shape derivatives of functionals subject to PDE constraints. We revisit the Lagrangian approach using the implicit functi…
Shape optimization for superconductors governed by H(curl)-elliptic variational inequalities
Antoine Laurain, Malte Winckler, Irwin Yousept
This paper is devoted to the theoretical and numerical study of an optimal design problem in high-temperature superconductivity (HTS). The shape optimization problem is to find an…
A shape optimization approach for electrical impedance tomography with point measurements
Yuri Flores Albuquerque, Antoine Laurain, Kevin Sturm
Working within the class of piecewise constant conductivities, the inverse problem of electrical impedance tomography can be recast as a shape optimization problem where the discon…
A level set-based structural optimization code using FEniCS
Laurain Antoine
This paper presents an educational code written using FEniCS, based on the level set method, to perform compliance minimization in structural optimization. We use the concept of di…
Properties of optimizers of the principal eigenvalue with indefinite weight and Robin conditions
Jimmy Lamboley, Antoine Laurain, Grégoire Nadin +1
In this paper, we are interested in the analysis of a well-known free boundary/shape optimization problem motivated by some issues arising in population dynamics. The question is t…
Distributed shape derivative via averaged adjoint method and applications
Antoine Laurain, Kevin Sturm
The structure theorem of Hadamard-Zolésio states that the derivative of a shape functional is a distribution on the boundary of the domain depending only on the normal perturbation…
Shape optimization of an electric motor subject to nonlinear magnetostatics
Peter Gangl, Ulrich Langer, Antoine Laurain +2
The goal of this paper is to improve the performance of an electric motor by modifying the geometry of a specific part of the iron core of its rotor. To be more precise, the object…
On a Bernoulli problem with geometric constraints
Antoine Laurain, Yannick Privat
A Bernoulli free boundary problem with geometrical constraints is studied. The domain $\Om$ is constrained to lie in the half space determined by and its boundary to co…